How do I use the exponential shift to solve the linear differential equation y'' + 7y' +12y = 2(e^-3)(cos2x)

- anonymous

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- anonymous

im looking to find the general solution y = yc +yp. so far i have solved the homogenous part of the equation yc. yc = Ae^-3x + Be^-4x. i cant solve for yp yet.

- anonymous

ok

- anonymous

Let me do it on paper first. I think it would be murder typing it out.

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- anonymous

haha thank you! any help will go a long way

- anonymous

i'll continue to try draw something out of my mess of numbers and letters while i wait

- anonymous

i also figured that the derivative operator 'D' helps so that the LHS = (D^2 + 7D +12)y

- anonymous

You do mean e^{-3x}, don't you?

- anonymous

yes! sorry typo

- anonymous

When I get to factors that need expanding, I'm going to get Mathematica to do that (save time).

- anonymous

ok no worries. if i dont follow il just let u know

- anonymous

So what happened, your lecturer just dump theory on you with no demonstration?

- anonymous

he demonstated with the d.e. y'' + 6y' + 13y = x(e^3x)(sin2x) however that takes y = imaginary(Y) and also takes into account the complex numbers. As my roots are reall -3, -4 and i take y=real(Y) instead, i dont know what yp to try

- anonymous

he pretty much chalk vomits all over the board without going into the specifics of how he gets to places

- anonymous

Not trained to teach...

- anonymous

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- anonymous

its really quite frustrating... luckily we are changing lecturers next week.. sorry for any hassle im causing you!

- anonymous

just give me a fan point and i'll be happy

- anonymous

wow thanks! im just gona go through it and check i understand.. haha ok sure how do i do that?

- anonymous

just click my 'become a fan' link...if there isn't one there, refresh the page...should work then

- anonymous

ps. is there a place to download mathmatica for free? ok right on it

- anonymous

www.wolframalpha.com
The guy who made mathematica made this site. It can do a lot of things like integration, solving differential equations, plotting, etc.

- anonymous

fanned. thanks a million! will i still be able to ask help from you if i have any more troubles..

- anonymous

this is wolfram's solution to your equation
http://www.wolframalpha.com/input/?i=y%27%27-2y%27%2B5y+%3D+16x^3*e^%283x%29+++

- anonymous

woops...no it's not...wait.

- anonymous

haha! i was like crap.. i did notttttt get that

- anonymous

http://www.wolframalpha.com/input/?i=y%27%27%2B7y%27%2B12y+%3D+2e^%28-3%29cos%282x%29

- anonymous

haha ur awesome at pen to paper but im afraid you did the same typo as me last time. theres an 'x' in e^-3x. however the graphs dont look how i thought they would..

- anonymous

graphs in the correct version*

- anonymous

ah...typo...

- anonymous

yep :) i thought it would have more of a decaying oscillation as it is overdamped.. is it because of the negative exponential? why?

- anonymous

So, am I right in understanding you've finished deriving the solution?

- anonymous

And you're reading off that and not Wolfram?

- anonymous

sorry no. i was comparing my notes to the graphs of wolfram.. but! i havent read through the wolfram content yet.. just making observations. if you would like you can continue helping other students.. and im guessing when i need help again it will notify you?

- anonymous

Yes, I get an e-mail if you respond to a thread I've been in.
Are you fine to derive the rest?

- anonymous

If an error's been made on my part, it's because it's after 1am where I am.
If you need help in the next ~12-24hrs, I may not be around. You'd should try your luck with someone else.

- anonymous

i should be ok for now thanks :) it takes me quite a while longer than you to come up with a solution

- anonymous

yep me too. 1:22am. ok do u recommend anyone else?

- anonymous

I don't know the particular skill level of people on here. You may have to post and cross fingers.

- anonymous

Is this an assignment due tomorrow or something?

- anonymous

ahah yeh you caught me out. due 2pm. i wish i could say im a more dedicated student working til the early hours of the morning doing maths... ah the thrills of life!

- anonymous

Well, since your timezone's mine, if I see something from you in the morning and I can respond, I will. My day will be hell busy, though.

- anonymous

Anyways, good luck. I seriously have to hit the sack.

- anonymous

thanks you are a hero! night!

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